In a multiple regression model, what is the assumed mean of the error term ε?

In a multiple regression model, it is assumed that the mean of the error term, denoted as ε, is 0. This assumption is fundamental because it implies that the errors are distributed randomly around the regression line, indicating that the model's predictions are unbiased on average.

When the mean of the error term is zero, it ensures that the predicted values made by the regression model do not systematically overestimate or underestimate the actual values. Instead, any deviations from the predicted values are due to random variation. This assumption is crucial for the validity of statistical inference derived from the model, such as hypothesis testing and the construction of confidence intervals.

If the mean of the error term were not zero, it would suggest that there is a consistent bias in the model's predictions, violating one of the key assumptions of ordinary least squares regression. Thus, setting the mean of the error term to zero helps ensure the reliability and interpretability of the regression results.